Liquid crystal device

ABSTRACT

Liquid crystal devices are described that exhibit bistable, tri-stable or other multistable operation. The stable liquid crystal configurations are attained using a surface alignment grating ( 144 ) on the internal surface of at least one cell wall ( 142 ). The surface profile of the surface alignment grating comprises three or more defect sites per grating period and permit the liquid crystal molecules to adopt any one of two or more stable pretilt angles in the same azimuthal plane. Application of a suitable voltage causes the liquid crystal material to switch between the stable configurations.

[0001] This invention relates to liquid crystal devices, in particularto nematic liquid crystal devices.

[0002] Liquid crystal devices (LCDs) typically comprise a thin layer ofa liquid crystal material contained between cell walls. Opticallytransparent electrode structures on the cell walls allow an electricfield to be applied across the liquid crystal layer causing are-ordering of the liquid crystal molecules.

[0003] To produce displays with a larger number of addressable elementsit is common to construct the liquid crystal device with a series of rowelectrodes on one wall and a series of column electrodes on the otherwall. In this way a matrix of separately addressable elements or pixelsis formed and a given voltage can be applied to each individual pixel inthe device by applying certain voltages to given rows and columns. Thetechnique of applying column and row voltage waveforms to switch eachpixel of the display in turn is termed multiplexing.

[0004] Twisted nematic (TN) liquid crystal devices are switched to an“on” state by application of a suitable voltage, and will switch back toan “off” state when the applied voltage falls below a certain level,i.e. these devices are monostable and loss of power leads to loss of theimage. TN displays can be constructed using stripes of row and columnelectrodes on the upper and lower cell surfaces allowing the device tobe multiplexed. The number of elements that can be addressed using rmsmethods is limited by the steepness of the device transmission vsvoltage curve as detailed by Alt and Pleschko in IEEE Trans ED vol ED 211974 pages 146-155. Incorporating a thin film transistor adjacent toeach TN pixel improves the total number of pixels which can beaddressed; such displays are termed active matrix. Active matrix TNdevices have several advantages compared with rms addressed TN displays,including a relatively low operating voltage requirement and a widetemperature operating range. This allows construction of small andportable battery powered displays for applications such as laptopcomputers.

[0005] In addition to monostable liquid crystal devices of the typedescribed above, devices are known where the liquid crystal can adopttwo stable configurations, i.e. the device is bistable. In such a deviceit is possible to switch between the bistable states by applying asuitable electrical signal. After the suitable electrical signal hasbeen applied, the liquid crystal switches into one of the two possiblestates and, until an electrical signal capable of switching the deviceinto the alternative bistable state is applied, the device will remainin that state. If switching between bistable states occurs at a welldefined voltage threshold, bistability also permits a high level ofmultiplexibility because, unlike monostable devices, there is no need tokeep a certain rms voltage level across each switched pixel.Additionally, conventional monostable LCDs are typically updated at30-60 times a second regardless of whether the display image ischanging. In contrast, a bistable display only needs to be updated whena new image is required. In the case of electronic paper with a viewingtime of 60 s per page, a bistable display might consume only 1/3600 ofthe power of a monostable display assuming similar operating voltagesand cell spacing etc. This would allow battery size (and weight) to besignificantly reduced.

[0006] Examples of bistable liquid crystal displays include surfacestabilised ferroelectric liquid crystal (SSFELC) devices as described byN A Clark and S T Lagerwall, Appl. Phys. Lett., 36, 11, 899 (1980). Ithas also been shown in Patent Applications WO 91/11747 (“Bistableelectrochirally controlled liquid crystal optical device”) and WO92/00546 (“Nematic liquid crystal display with surface bistabilitycontrolled by a flexoelectric effect”) that a nematic can be switchedbetween two stable states via the use of chiral ions or flexoelectriccoupling.

[0007] In WO 97/14990 it is shown how a zenithally bistable nematicdevice may be constructed using a grating of a given design such thatthe liquid crystal molecules can adopt two stable pretilt angles in thesame azimuthal plane. The term “same azimuthal plane” is explained asfollows: let the walls of a cell lie in the x, y plane, which means thenormal to the cell walls is the z axis hence two pretilt angles in thesame azimuthal plane means two different molecular positions in the samex, z plane. One of these states is a high pretilt state, whilst theother is a low pretilt state. The difference in energy between thestates is minimised by altering the grating pitch and grating groovedepth ratio for a grating of a given asymmetry, producing bistabilityover a range of grating conditions. This allows a device to be producedwhich can adopt either of two stable liquid crystal configurations. Itis also demonstrated how a zero pretilt defect state, with an associatednon-defect state, may be induced by a symmetrical sinusoidal gratingsurface.

[0008] The two zenithally stable liquid crystal configurations of WO97/14990 persist after the driving electrical signals have been removedand the device has been shown (Wood et. al. SID Digest 00) to be highlyresistant to mechanical shock, provide microsecond latching times at lowdriving voltages (<20V) and allow a high degree of multiplexability.WO99/34251 teaches another zenithally bistable device having a negativedielectric anisotropy material in a twisted nematic configuration.

[0009] Strictly, all bistable displays will only exhibit two stablestates. In such liquid crystal devices, combinations of externalpolarisers, for example, can be arranged so that one of the statesproduces a dark (or “off”) state whilst the other states produces alight (or “on”) state. In many applications, such as TV displays, thereis the requirement for grey-scale in addition to the “dark” and “light”states. This is commonly achieved using either temporal or spatialdither, or some combination of both with bistable technologies such assurface stabilised ferroelectric devices.

[0010] Temporal dither utilises variations of liquid crystal “dark” and“light” states for each pixel with time. Greyscale is achieved byswitching each pixel “on” and “off” at a rate faster than the viewer canperceive. The average time the pixel is in the “light” state rather thanthe “dark” state determines the grey-level perceived. Temporal ditherrequires the liquid crystal to be switched at a faster rate, andtherefore has disadvantages in that faster optical response times arerequired from the liquid crystal and the power consumption of thedisplay is increased.

[0011] Spatial dither is achieved by having each pixel comprising two ormore sub-pixel regions. These sub-pixels can be of the same area orweighted with respect to each other and switching certain combinationsof the sub-pixels to the “on” and “off states gives the perception of anoverall grey level (e.g. a level with intensity in-between that of the“on” and “off” states for the pixel).

[0012] Spatial dither techniques require displays to be fabricated witha number of sub-pixel areas per pixel; this has the disadvantage ofincreased device fabrication complexity. Spatial dither also requiresthe use of separate electrical driving circuitry for each row and/orcolumn of sub-pixels, adding to the overall complexity and cost of theelectronics required to drive the device. In addition, spatial ditherreduces the overall aperture ratio of the pixel, leading to acorresponding reduction in the maximum reflectivity or transmissionassociated with the device. The requirement to include separate rowand/or column electrodes for the additional sub-pixels typicallyrequires the electrode track width to be reduced, thereby increasing theelectrical track resistance. This increases the power consumption of thedisplay and can lead to non-uniformities of the display as theaddressing signals change from one end of a line to the other.

[0013] Analogue (or domain) greyscale is also known where partial, orincomplete, switching of domains within a pixel is used so thatdifferent grey-levels can be formed from varying the number and/or sizeof domains in the pixel. This has been used in ferroelectric liquidcrystals and bistable cholesterics.

[0014] The principal disadvantage associated with the use of domaingrey-scale is that there is no operating window for the addressingwaveform; that is, each grey-level is achieved with a specificaddressing waveform. Ensuring the desired waveform is applied to aparticular pixel is problematical because changes to the waveformapplied to the rows and/or columns may arise due to losses along theresistive electrodes, variations caused by the temperature of thedriving circuitry (which will depend on use and therefore will varyacross the panel) or batch differences for the driving circuits. Changesin the response of the liquid crystal to the same field may also occuracross the device arising, for example, from variations of cell gap,alignment, thickness of alignment layer, cell temperature, alignment ofthe liquid crystal, and possibly image history. Any such deviationscause a change in the electro-optic response, and hence an error in theobserved analogue grey level.

[0015] Multiple threshold devices are also known, and have been used toattain analogue greyscale. In such devices, each pixel is sub-dividedinto areas which respond differently to applied electric fields; forexample by forming holes in the electrodes, including passive dielectriclayers or inducing alignment variations etc. One example of inducingmultiple threshold is provided in Bryan-Brown et al, (1998) proceedingsof Asia Display, p1051-1052, where it is demonstrated that grey-scalemay be achieved in a zenithally bistable device using a chirped gratingthat allows partial switching of an area of a pixel.

[0016] Multiple threshold techniques overcome, to a limited extent, thedisadvantages associated with the analogue greyscale techniquesdescribed above. However, sub-dividing each pixel into areas withdifferent switching characteristics adds substantial cost and complexityto the device. Moreover, it can lower the effective resolution of thedevice and can also lead to unwanted image artefacts for certain imagepatterns.

[0017] U.S. Pat. No. 4,333,708 describes how bistable nematic devicescan be constructed using various surface boundary conditions. Thebistability relies on the formation of defects at certain positions invarious cell geometries and it is the cell itself that is bistable; notthe individual cell surfaces. The different liquid crystalconfigurations are selected by applying certain combinations of voltagesin the plane of the cell and perpendicular to the plane of the cellwhich causes reorientation of the bulk configurations of the liquidcrystal. U.S. Pat. No. 4,333,708 also describes how a plurality ofbistable devices, each having a particular surface boundary conditions,can be combined in a single display to achieve grey-scale. Such adisplay would prove highly complex to manufacture.

[0018] U.S. Pat. No. 5,625,477 describes how a cholesteric liquidcrystal can form either a planar texture or a focal conic texture in anappropriate cell. The cholesteric pitch is chosen so that the planartexture reflects half the incident light, whilst the focal conic texturetransmits all the light and leads to a black state if the sample back isblackened. Selection of the alignment state is controlled by theamplitude the applied voltage pulse, and it was shown that the relativeproportions of domains adopting the planar or focal conic texture withina pixel area can be varied by applying voltage pulses of differentdurations. Disadvantages of this device include difficulties associatedwith obtaining greyscale and colour.

[0019] It is an object of the present invention to provide a liquidcrystal device with inherent greyscale that mitigates some of thedisadvantages, as described above, that are associated with obtaininggreyscale using spatial or temporal dither techniques.

[0020] According to the first aspect of this invention a liquid crystaldevice capable of adopting at least two stable states comprises a layerof liquid crystal material located between two cell walls, a means ofapplying a voltage to the liquid crystal layer and a surface alignmentgrating on the internal surface of at least one cell wall wherein thesurface profile of the surface alignment grating comprises three or moredefect sites per grating period with at least one +½ defect site pergrating period and at least one −½ defect site per grating period sothat the liquid crystal molecules can adopt any one of two or morestable pretilt angles in the same azimuthal plane in the locality of thesurface and wherein the arrangement is such that two or more stableliquid crystal molecular configurations can exist and whereinapplication of a suitable voltage causes the liquid crystal to adopt anyone of two or more stable configurations.

[0021] In one embodiment of this invention the liquid crystal moleculescan adopt any one of three or more stable pretilt angles in the sameazimuthal plane in the locality of the surface and wherein thearrangement is such that three or more stable liquid crystal molecularconfigurations can exist and wherein application of a suitable voltagecauses the liquid crystal to adopt any one of three or more of thestable configurations. Preferably, one pair of +½ and −½ defect sitesare situated so as to impart a low surface pretilt for one defect state.

[0022] This invention thus provides a liquid crystal device which can beswitched between a plurality of different stable configurations.Therefore an inherent grey-scale capability is provided which overcomesthe disadvantages associated with the spatial and temporal dithertechniques described above. Furthermore, an additional advantage of thisinvention is that a low surface pretilt defect state can be formed whichallows devices to be constructed that exhibit high optical contrastbetween the low surface pretilt defect state and any higher surfacepretilt states. This device could also be used for phase modulation oflight, for example it could be used as a Spatial Light Modulator.

[0023] In another embodiment of the invention, the low surface pretiltstate is of a significantly lower energy than that of any of the otherpossible defect states, wherein only the non-defect state and the defectstate of low pretilt can be readily selected on application of avoltage. Accordingly, this invention provides a bistable device with adifference in surface pretilt of substantially 90° between the lowsurface pretilt defect state and the high surface pretilt non-defectstate, thereby providing optimum optical contrast between the twostates. This has the advantage over the previous bistable devicedescribed in WO 97/14990 that a highly symmetrical grating is notrequired; the requirements for the grating design are that the defectsites are appropriately positioned. The calculation of the energyassociated with a particular grating design, and the pretilt induced bysuch a grating design are subsequently described herein.

[0024] Conveniently, the surface alignment grating structure is treatedwith, or formed from, a material that induces a homeotropic alignment ofthe liquid crystal director with respect to the local surface direction.Various methods of inducing homeotropic alignment are well known.

[0025] Alternatively, the surface alignment grating structure is treatedwith, or formed from, a material that induces a planar alignment of theliquid crystal director with respect to the local surface direction.Various methods of inducing planar alignment are well known.

[0026] In further preferred embodiments, one cell wall has a surfacealignment grating structure and the other cell wall has a surface whichinduces homeotropic alignment of the liquid crystal or induces planarhomogenous alignment of the liquid crystal. Additionally, both cellwalls may have surface alignment grating structures.

[0027] The liquid crystal material may be a nematic liquid crystalmaterial, in particular nematic liquid crystal material with a positivedielectric anisotropy. If the surface alignment grating structure istreated with, or formed from, a material that induces a planar alignmentof the liquid crystal director with respect to the local surfacedirection a nematic liquid crystal material with a negative dielectricanisotropy is preferred. The term nematic liquid crystal is taken hereinto include long pitch cholesteric materials.

[0028] Preferably the pitch of the surface alignment grating structureis within the range of 0.1 μm to 10 μm. More preferably the pitch isgreater than 500 nm, more preferably the pitch is greater than 800 nmand more preferably the pitch is greater than 1000 nm. Furthermore, itis convenient for the pitch to be less than 5 μm and more convenient forthe pitch to be less than 2 μm.

[0029] Advantageously, the groove depth of the surface alignment gratingstructure is within the range of 0.05 μm to 3 μm and the two cell wallsare separated by between 1 μm to 20 μm.

[0030] In one embodiment of the invention a means of applying aplurality of voltages to the liquid crystal layer comprises a layer ofelectrically conductive, and substantially optically transparent,material applied to the internal surface of both cell walls. Furthermorethe layers of electrically conductive material applied to the internalsurface of both cell walls may be patterned so as to produce an array(or matrix) of addressable pixels. The electronics required to passsuitable electrical signals to an array of addressable pixels (i.e.multiplexing a matrix device) would be well known to a person skilled inthe art.

[0031] In another embodiment of the invention the liquid crystal devicefurther comprising a means for optically distinguishing between at leasttwo of the stable liquid crystal configurations adopted. The means foroptically distinguishing between at least two of the liquid crystalconfigurations may comprise a pair of polarisers placed one either sideof the liquid crystal device with their respective optic axes alignedwith respect to the liquid crystal device such that the amount of lighttransmitted through the liquid crystal display will differ depending onwhich liquid crystal configuration is adopted, an optically reflectivelayer placed one side of the liquid crystal device and a polariserplaced the other side of the liquid crystal device with its optic axisaligned with respect to the liquid crystal device such that the amountof light reflected by the device will differ depending on which liquidcrystal configuration is adopted, or a dichroic dye, the dye being addedto the liquid crystal such that the amount of light absorbed by theliquid crystal display will differ depending on which liquid crystalconfiguration is adopted. Many other methods of optical distinguishingbetween the liquid crystal configurations, such operating the device ina scattering mode as described in GB patent application 9928126.3, arewell known to persons skilled in the art.

[0032] According to a second aspect of this invention, a multi-stableliquid crystal device comprises a layer of liquid crystal materiallocated between two cell walls and a means of applying a voltage to theliquid crystal material wherein a surface alignment grating structure onthe internal surface of at least one cell wall has a surface profilewhich is such so as to induce the liquid crystal molecules to adopt anyof three or more stable pretilt angles in the same azimuthal plane andwherein the arrangement is such that three or more stable liquid crystalmolecular configurations can exist and wherein application of a suitablevoltage causes the liquid crystal material to adopt any one of three ormore stable configurations. In a preferred embodiment three differentpretilt angles in the same azimuthal plane can be adopted.

[0033] As described above, having three or more stable liquid crystalconfigurations is advantageous in obtaining greyscale.

[0034] As described above a low surface pretilt state, and a highsurface pretilt state, allows optimum optical contrast be achieved. Thusaccording to a third aspect of this invention, a bistable liquid crystaldevice comprises a layer of liquid crystal material located between twocell walls, a means of applying a voltage to the liquid crystal layerand a surface alignment grating on the internal surface of at least onecell wall wherein the surface profile of the surface alignment gratingcomprises three or more defect sites per grating period with at leastone +½ defect site per grating period and at least one −½ defect siteper grating period wherein one pair of +½ and −½ defect sites aresituated so as to impart low surface. pretilt in the azimuthal plane toone defect state wherein such low pretilt state is of a significantlylower energy than that of any of the other possible defect stateswherein only the non-defect state and the defect state of low surfacepretilt can be readily selected on application of a voltage. Low surfacepretilt can be considered to be lower than 20°, preferably lower than10° and more preferable less than 5°.

[0035] The concept of liquid crystal defects, liquid crystal defectstates and an explanation of the physical properties of a gratingstructure which cause defects to form (termed “defect sites”) as usedabove are well known to a person skilled in the art and are described inmore detail below.

[0036] The invention will now be described, by way of example only, withreference to the accompanying drawing of which;

[0037]FIG. 1 shows a cross section of the two possible liquid crystaldirector configurations (with contour line representation of thedirector field) on the grating surface of a zenithal bistable device asdescribed in WO 97/14990;

[0038]FIG. 2 (prior art) shows a cross section of a cell configurationwhich allows bistable switching between the two states of the embodimentof the zenithal bistable device of FIG. 1;

[0039]FIG. 3 shows a cross section of an asymmetric grating structureindicating defect sites;

[0040]FIG. 4 shows a geometrical interpretation of ρ in the z-plane;

[0041]FIG. 5 shows various grating profiles and the, calculated energyof the various states;

[0042]FIG. 6 shows a cross section of a symmetric grating surface withthree defects sites per unit length;

[0043]FIG. 7 shows a cross section of a symmetric grating surface withfour defect sites per unit length;

[0044]FIG. 8 shows a cross section of a a) symmetric and b) anasymmetric grating surface having at least one substantially zeropretilt alignment state;

[0045]FIG. 9 shows a cross section of a grating surface with 8 defectsites per unit length;

[0046]FIG. 10 shows a cross section of a) an asymmetric blazed grating,b) an asymmetric blazed grating having two distinct sub-grating elementsof different pitch per unit length, c) an asymmetric blazed gratinghaving two distinct sub-grating elements of different amplitude per unitlength and d) an asymmetric blazed grating having two distinctsub-grating elements of different amplitude and pitch per unit length;

[0047]FIG. 11 shows a cross-section of the grating of FIG. 10(b), andfurther shows three of the six possible liquid crystal configurationsthat may form on such a grating;

[0048]FIG. 12 shows a cross-section of the grating of FIG. 10(d), andfurther shows three of the six possible liquid crystal configurationsthat may form on such a grating;

[0049]FIG. 13 shows a cross section of a cell configuration,incorporating one multi-stable surface, which allows selection of thenon-defect and multiple defect states;

[0050]FIG. 14 shows a cross sectional SEM image of a holographicallydefined symmetric grating;

[0051]FIG. 15 shows a cross sectional SEM image of aphotolithographically defined symmetric grating;

[0052]FIG. 16 shows the measured pretilt induced to a nematic liquidcrystal, by the photolithographically defined symmetric grating, as afunction of grating exposure. (corresponding to track number);

[0053]FIG. 17 shows a cross sectional SEM image of a grating surfaceused to form a tri-stable device;

[0054]FIG. 18 shows a cross section of the cell and associated liquidcrystal configuration of the tri-stable device;

[0055]FIG. 19 shows a schematic plan view of two designs of mask thatmay be used to create an alternating groove grating structure;

[0056]FIG. 20 shows a cross sectional SEM image of a grating fabricatedusing a mask of the design shown in FIG. 19;

[0057]FIG. 21 is a graphical representation of the measuredtransmission, as a function of applied voltage, of a deviceincorporating the grating shown in FIG. 20; and

[0058]FIG. 22 is a graph of the measured voltage and pulse widthsrequired to attain any of three stable device configurations of thetri-stable device; and

[0059]FIG. 23 is a schematic illustration of the transmission versusapplied electrical energy characteristics of prior art devices comparedwith the characteristics of a tri-stable device according to the presentinvention.

BACKGROUND

[0060] To put the present invention into context, a description of thezenithal bistable device of WO 97/14990 will be given with reference toFIGS. 1 and 2 wherein a liquid crystal layer (1) is in contact with anasymmetric surface alignment grating (1) of pitch W and groove depth h.The liquid crystal director is denoted by the vector n. The contourlines (3) are perpendicular to orientation of the liquid crystaldirector (n) and the grating surface has been treated, for example bycoating with a homeotropic surfactant (not shown), to induce localhomeotropic alignment of the liquid crystal at the interface (4) betweenthe liquid crystal layer (2) and the surface alignment grating (1).

[0061] The term homeotropic takes the meaning, well known to a personskilled in the art, that the director (n) is oriented substantiallyperpendicularly to the local surface and herein a surface alignmentgrating is taken to mean an array of repeating elements of a unitlength, as would be understood by a person skilled in the art. Hereinthe term “same azimuthal plane” is explained as follows: let the wallsof a cell lie in the x, z plane, which means the normal to the cellwalls is the y axis. Two pretilt angle in the same azimuthal plane meanstwo different molecular positions in the same x, y plane. Herein, asdefined in FIG. 1, the term pretilt shall mean the tilt of the directoraway from the x-z plane at some distance away from the surface where thedirector is invariant in the x-z plane; hence perfectly planar alignmentgives zero pretilt and perfectly homeotropic alignment gives 90°pretilt.

[0062] It was demonstrated in a particular embodiment of WO 97/14990that a nematic liquid crystal in contact with an alignment gratingsurface coated with a homeotropic surfactant can adopt either anon-defect (FIG. 1a) or defect (FIG. 1b) alignment configuration. Liquidcrystal defects can, in simple terms, be considered as a local area ofdiscontinuity in the director field and are well known to personsskilled in the art. A summary of the theory relating to liquid crystaldefects and disclinations can be found in P. G. deGennes, “The physicsof liquid crystals” (Clarendon press, 1974).

[0063] In the non-defect structure of figure la the nematic liquidcrystal will, at the interface (4) between the surface alignment grating(1) and the liquid crystal (3), orient so as to be substantiallyperpendicular to the local surface of the grating (1). Within a shortdistance of the grating-liquid crystal interface (4), compared with theoverall thickness of the liquid crystal cell, the liquid crystal willadopt a homeotropic alignment configuration of θ_(p)≈90°.

[0064] In the defect structure of FIG. 1b, so-called defects of strength−½ (5) will form in the vicinity of concave defect sites (7) andso-called defects of strength +½ (6) will form in the vicinity of convexdefect sites (8). The result of the formation of the +½ and −½ defectpair is that within a short distance of the grating-liquid crystalinterface (4), as compared with the overall thickness of the liquidcrystal cell, the nematic liquid crystal will adopt a configuration of apretilt (in this example θ_(p≈)45°) lower than that formed for thenon-defect structure of FIG. 1a. Note that defects can only occur inpairs, and each pair must be of an equal and opposite magnitude. A morecomplete explanation of defects of strength +½ and −½ can be found in P.G. deGennes, “The physics of liquid crystals” (Clarendon press, 1974),and would be known by a person skilled in the art.

[0065] Herein, defects of strength of approximately −½ (within a rangeof −1 to 0) and +½ (within a range of 0 to 1) are termed the “−½ defect”and the “+½ defect” respectively. The positions on a grating surfacewhere +½ and −½ defects form are associated with regions of convex andconcave minimum radii of curvature of the grating surface. The terms “−½defect site” and “+½ defect site”, are taken to mean the region on agrating surface where a person skilled in the art would reasonablyexpect either a −½ or +½ defect to form using common general knowledge,documents such as P. G. deGennes, “The physics of liquid crystals”(Clarendon press, 1974), and the teachings contained hereinafter. Theterm “defect site” means either a −½ defect site or a +½ defect site and“defect sites” is simply more than one such defect site.

[0066] A suitable cell configuration to exploit the existence of thebistable surface described with respect to FIG. 1, is shown in crosssection in a stylised form in FIG. 2. The cell configuration of FIG. 2comprises a layer of nematic liquid crystal material with a positivedielectric anisotropy (2) sandwiched between a first glass wall (9) anda second glass wall (10). The first glass cell wall (10) is treated, forexample by coating with lecithin (not shown), to induce homeotropicalignment of the nematic liquid crystal at the glass cell wall andliquid crystal interface (11). The second glass cell wall (10) is coatedwith a bistable surface alignment grating (1), the profile of which isas described with respect to FIG. 1.

[0067] The device of FIG. 2 allows the liquid crystal molecules to adopteither of two stable configurations, as shown in FIGS. 2a and 2 b.

[0068] In FIG. 2a, homeotropic alignment of the liquid crystal isinduced at the first substantially flat cell wall surface (9) because ofthe homeotropic treatment (not shown). At the second cell wall (10) theliquid crystal (2) adopts a non-defect state (as described with respectto FIG. 1a) and induces homeotropic alignment of the liquid crystal (2)within a short distance, with respect to the overall thickness of theliquid crystal cell (d), of the grating-liquid crystal interface (4). Auniform homeotropic (high tilt) alignment of the liquid crystal isobtained throughout the bulk of the cell.

[0069] In FIG. 2b, homeotropic alignment of the liquid crystal isobtained at the first substantially flat cell wall surface (9) becauseof the homeotropic treatment (not shown). At the second cell wall (10)the surface alignment grating (1) adopts a defect state (as describedwith respect to FIG. 1b) and induces low tilt alignment (in this exampleθ_(p≈)45°) of the liquid crystal (2) within a short distance, withrespect to the overall thickness of the liquid crystal cell (d), of thegrating-liquid crystal interface (4). A splayed liquid crystal structureis thus formed. For many nematic materials, a splay or bend deformationwill lead to a macroscopic flexoelectric polarisation, which isrepresented by the vector P in FIG. 2. A dc pulse is used to couple tothis polarisation and depending on its sign will either favour ordisfavour the configuration of FIG. 2(b). The application of pulses ofpositive and negative sign can be used to drive the system between thetwo stable states.

[0070] Simple Model of Grating Induced Surface Pretilt

[0071] The pretilt associated with a particular pair of +½ and −½defects has been found to depend on the relative positions of the +1/2and −½ defects per grating period. A model of the pretilt induced at asurface by a grating structure will now be described with reference toFIGS. 1 to 3.

[0072] Consider a nematic liquid crystal restricted in a configurationsuch that at all points the director of the liquid crystal is parallelto the x-y plane. Let θ(x, y) be the tilt angle between the director at(x,y) and the x-axis. Then, in an untwisted configuration, θ(x, y)completely specifies the director field.

[0073] The static director field is governed by a torque balanceequation obtained from minimising the Frank-Oseen free energy of anematic liquid crystal. Under planar configuration and taking anapproximation that the splay and bend elastic constants are equal, boththe Frank-Oseen free energy expression and the corresponding torquebalance equation can be reduced to a simple form as: $\begin{matrix}{G = {\frac{K}{2}{\int\quad {{x}{y}\left\{ {\left( \frac{\partial\theta}{\partial x} \right)^{2} + \left( \frac{\partial\theta}{\partial y} \right)^{2}} \right\}}}}} & (1) \\{0 = {\left( {\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}}} \right)\theta}} & (2)\end{matrix}$

[0074] where G is the Frank-Oseen free energy per unit length and K isthe bend or splay elastic constant. The torque balance equation 2 issimply the Laplace equation. It is well-known in complex variables thatany analytic function is a solution to the Laplace equation. Inparticular, if we seek solutions for a configuration of disclinationlines normal to the x-y plane, the problem is directly analogous to thepotential flow fluid mechanics or two dimensional electrostatics; seefor example M. R. Speigel, “theory and problems of complex variables”(Schaum, New York, 1964) and P. M. Morse and H. Feshbach, “Methods oftheoretical physics” (McGraw-Hill, New York, 1953). The equivalents ofthe disclination lines are the line sources or sinks in potential flowfluid mechanics and line charges in two dimensional electrostatics.

[0075] For an isolated disclination core at the origin and with theboundary condition that the directors are un-anchored at infinity,solution to the Laplace equation 2 is given by: $\begin{matrix}{\theta = {{\frac{M}{2}\left\{ {\ln \left( {x + {iy}} \right)} \right\}} + \alpha}} & (3) \\{{= {{\frac{M}{2}{\tan^{- 1}\left( \frac{y}{x} \right)}} + \alpha}}\quad} & (4)\end{matrix}$

[0076] where

denotes the imaginary part of a complex function, M/2 is the strength ofthe disclination and the angle, α, is an arbitrary constant ofintegration. m is an integer necessary to ensure that the directororientation is preserved in any close circuit which enclosed thedisclination core at the origin. Equation 3 is well-known as the streamline function in potential flow fluid mechanics or the flux linefunction in two dimensional electrostatics.

[0077] Having obtained the tilt function of 2 for the director field,the free energy 1 can be readily evaluated, see for example P. G.deGennes & J Prost, “The physics of liquid crystals” (Academic, NewYork, 1993), to yield: $\begin{matrix}{G = {\frac{K\quad \pi}{4}M^{2}{\ln \left( \frac{R}{\lambda} \right)}}} & (5)\end{matrix}$

[0078] where R is the dimension of the system and λ is the disclinationcore radius, and is typically the order of a few molecular lengths(circa 100 Å). Note that the free energy, G, diverges logarithmicallywith the system size.

[0079] If a configuration of parallel disclination lines with theircores pinned at the points (a₁, b₁), . . . , (a_(n), b_(n)) . . . in thex-y plane is considered, then the tilt angle θ(x, y) which specifies thedirector field is the superposition of the contributions from eachindividual disclination lines is: $\begin{matrix}{{\theta = {{\sum\limits_{n}{\theta_{n}\left( {x,y} \right)}} + \alpha}}\quad {where}} & (6) \\{\theta_{n} = {\frac{M_{n}}{2}\left\{ {\ln \left( {x - a_{n} + {i\left( {y - b_{n}} \right)}} \right)} \right\}}} & (7) \\{{= {\frac{M_{n}}{2}{\tan^{- 1}\left( \frac{y - b_{n}}{x - a_{n}} \right)}}}\quad} & (8)\end{matrix}$

[0080] θ_(n) defines the director field due an isolated disclinationline of strength M_(n)/2 pinned at (a_(n),b_(n)). Similarly, the freeenergy, G, is also the sum of all individual contributions:$\begin{matrix}{{G = {\frac{K}{2}{\int{{x}{y}{{\sum\limits_{n}\left( {\frac{\partial\theta_{n}}{\partial x},\frac{\partial\theta_{n}}{\partial y}} \right)}}^{2}}}}}\quad} & (9) \\{= {{\frac{K\quad \pi}{4}{\sum\limits_{n}{M_{n}^{2}{\ln \left( \frac{R}{\lambda} \right)}}}} + {\frac{K}{2}{\sum\limits_{n \neq n^{\prime}}{\int_{r_{n\quad n^{\prime}}}^{R}{\left\{ \theta_{n} \right\} \left( \frac{M_{n^{\prime}}}{2} \right)\quad \frac{r}{r}}}}}}} & (10) \\{{= {{\frac{K\quad \pi}{4}\left( {\sum\limits_{n}M_{n}} \right)^{2}{\ln \left( \frac{R}{\lambda} \right)}} + {\frac{K\quad \pi}{4}{\sum\limits_{n \neq n^{\prime}}{M_{n}M_{n^{\prime}}{\ln \left( \frac{R}{r_{n\quad n^{\prime}}} \right)}}}}}}{where}} & (11) \\{{r_{n\quad n^{\prime}} = {{\left( {a_{n},b_{n}} \right) - \left( {a_{n^{\prime}},b_{n^{\prime}}} \right)}}}\quad} & (12)\end{matrix}$

[0081] Equation 3 is a generalisation of the case of a pair ofdisclination lines as described in, for example, P. G. deGennes & JProst, “The physics of liquid crystals” (Academic, New York, 1993). Theintegral in equation 10 is obtained by an integration by partstechnique. The integral is performed along a cut from (a_(n),b_(n)) inthe direction of (a_(n),b_(n))-(a_(n)′,b_(n)′). Along the cut, θ_(n)goes through a discontinuous change of 2πM_(n) as one traverses acrossthe cut in the anti-clockwise direction. Evaluated the integral 10yields equation 11 for the free energy. As noted in P. M. Chaikin & T.C. Lubensky, “Principles of condensed matter physics” (CambridgeUniversity Press, 1995), the 1nR divergence in part of equation 11 canbe eliminated if the sum of the strengths of all disclination lines inthe system is zero.

[0082] Consider a simple case in which an infinite array of disclinationlines each with strength ±M/2 are pinned at regular interval of L atpositions ±(a−nL, b) where n is an integer in the range [−∞, ∞]. Letz=x+iy and c=a+ib. By using equation 6, one obtains the tilt anglefunction for the director field: $\begin{matrix}{\theta = {{\frac{M}{2}{\sum\limits_{n = {- \infty}}^{\infty}\quad {\left\{ {\ln \left( {z - c - {nL}} \right)} \right\}}}} - {\frac{M}{2}{\sum\limits_{n = {- \infty}}^{\infty}\quad {\left\{ {\ln \left( {z + c - {nL}} \right)} \right\}}}} + \alpha}} & (13) \\{{= {{\frac{M}{2}\left\{ {\ln \left\lbrack {\frac{z - c}{z + c}{\prod\limits_{n = 1}^{\infty}\frac{1 - \left( \frac{z - c}{nL} \right)^{2}}{1 - \left( \frac{z + c}{nL} \right)^{2}}}} \right\rbrack} \right\}} + \alpha}}\quad} & (14) \\{{= {{\frac{M}{2}\left\{ {\ln \left\lbrack \frac{\sin \quad \frac{\pi}{L}\left( {z - c} \right)}{\sin \quad \frac{\pi}{L}\left( {z + c} \right)} \right\rbrack} \right\}} + \alpha}}\quad} & (15)\end{matrix}$

[0083] Equation 15 was obtained from equation 14 by using the infiniteproducts expansion of the sine function as in, for example, P. M. Morseand H. Feshbach, “Methods of theoretical physics” (McGraw-Hill, NewYork, 1953). In regions far from the array, $\begin{matrix}{{\lim\limits_{y\rightarrow{\pm \infty}}\theta} = {{{\pm \frac{M}{2}}\left\{ {{\tan^{- 1}\left\lbrack \frac{\tan \frac{\pi}{L}\left( {x - a} \right)}{\tanh \frac{\pi}{L}{y}} \right\rbrack} - {\tan^{- 1}\left\lbrack \frac{\tan \frac{\pi}{L}\left( {x + a} \right)}{\tanh \frac{\pi}{L}{y}} \right\rbrack}} \right\}} + \alpha}} & (16) \\{{= {{{\pm \frac{M}{2}}\left\{ {\pi \quad \frac{2a}{L}} \right\}} + \alpha}}\quad} & (17)\end{matrix}$

[0084] From equation 17 it can be seen that the grating will induce zeropretilt when a =L/2. Thus for a symmetrical sinusoidal grating, asdescribed in WO 97/14990, +½ and −½ defects will form along the gratingequally spaced by the distance a (which is half the grating pitch lengthL). This defect configuration produces a zero pretilt defect state.

[0085] Referring to FIG. 3, if within one period of the grating there isonly one position of maximum curvature which is convex and only onewhich is concave and the zero pretilt condition a=L/2 is not fulfilled(in this case because the grating is asymmetric) the alignment gratingwill induce a finite surface tilt. For the asymmetric grating structureof FIG. 3, +½ defects will form at the +½ defect sites (21) and −½defects will form at the −½ defect sites (22) and the surface alignmentgrating will impart a pretilt to the liquid crystal, within a shortdistance of the surface compared to the overall cell thickness,according to equation 17.

[0086] From the model described above it can been seen that it is theposition of defect pair formation, and not the degree of symmetry of thegrating surface, which determines, the surface pretilt that is impartedto a liquid crystal layer by a surface alignment grating at a shortdistance from the grating surface.

[0087] Detailed Model of Grating Induced Surface Pretilt.

[0088] A more rigorous analytical model of the liquid crystal pretiltinduced by the formation of defects on a surface alignment grating willnow be described.

[0089] Theoretical examples derived from the model will then bedescribed. with reference to FIGS. 4 and 5.

[0090] Surface deformation of a nematic liquid crystal due to the shapeof a surface interface have been investigated. Only interfaces with aperiodic profile and homeotropic surface alignment of the liquid crystalare considered. For smooth surfaces with no kink, surface line defectswith integral π topology nucleated on the interface surface can havefull translational freedom on the surface. The model describedhereinafter analyses the energetics of the line surface defects. Underequal elastic approximation and assumed planar director field, the onlyrelevant field variable for the director field is the tilt angle θ ofthe director and the governing static equation is the Laplace equation.By means of a conformal mapping techniques, θ and the surfacedeformation energy can be obtained without the small amplitudeapproximation used by Berreman (W. D. Berreman, Phys. Rev. Lett. 28,1683 (1972)) and deGennes (P. G. deGennes, “Physics of liquid crystals”,Oxford, 77 (1974)). Unlike Barbero (G. Barbero, Lett Nuovo Cimento, 29,553 (1980)), only smooth surfaces are considered and hence there is nosurface defect pining.

[0091] Let w=u+iv be the conformal co-ordinates of the transformedz=x+iy co-ordinates such that v=0 corresponds to the surface profiley=f(x). Consider an array of surface line defects of alternatingstrength ±mπ at the positions λ_(±)+2πn where n=(−∞, ∞) on the =0 line.The total surface deformation energy per period per unit length for asurface with a periodic maximum and minimum energy is: $\begin{matrix}{g = {\frac{K}{2L}{\int_{0}^{\infty}\quad {{v}{\int_{0}^{L}\quad {{u}\left\{ {{\frac{\partial\rho}{\partial u}\frac{\partial\theta}{\partial v}} - {\frac{\partial\rho}{\partial v}\frac{\partial\theta}{\partial u}}} \right\}}}}}}} & (18) \\{{\approx {\frac{K}{2L}\pi \left\{ {\left\lbrack {{\max (\rho)} - {\min (\rho)}} \right\rbrack + {{m}\left\lbrack {{\rho \left( \lambda_{+} \right)} - {\rho \left( \lambda_{-} \right)}} \right\rbrack} + {{m}^{2}{\ln \left\lbrack \frac{\sin^{2}\left( {\left( {\lambda_{+} - \lambda_{-}} \right)/2} \right)}{\sin^{2}\left( {a/2} \right)} \right\rbrack}}} \right\}}}\quad} & (19)\end{matrix}$

[0092] where ρ is the harmonic conjugate of θ and a is the radius of thedefect line core measured in w. The first square bracket term ofequation 19 is the nematic deformation energy without any defect. Themiddle square bracket term of equation 19 is due to the coupling of thedefect and non-defect deformation. The last term of equation 19 dependsonly on the defects. With g, the energetic stability of the defect canbe analysed with respect to the variation of λ_(±) and m. The directorconfiguration is specified by the tilt angle: $\begin{matrix}{{\rho + {i\quad \theta}} = {{\ln \frac{w}{z}} + {\sum\limits_{\alpha = \pm}{\alpha {m}\ln \quad {\sin \left( \frac{w - \lambda_{\alpha}}{2} \right)}}} + {i\quad \theta_{0}}}} & (20)\end{matrix}$

[0093] where θ₀ is the alignment angle of the director at the interface(i.e. local) surface.

[0094] In the limit ν=∞, hence $\begin{matrix}{{\lim\limits_{v\rightarrow\infty}\theta} = {{\sum\limits_{\alpha_{\pm}}{\alpha {m}{Im}\left\{ {\ln\left\lbrack \quad {\sin \left( \frac{w - \lambda_{\alpha}}{2} \right)} \right\rbrack} \right\}}} + \theta_{0}}} & (21) \\{{= {{{- {m}}\left( \frac{\lambda_{+} - \lambda_{-}}{2} \right)}\quad + \theta_{0}}}\quad} & (22)\end{matrix}$

[0095] If a periodic surface profile, with a multitude of maxima andminima within a single period, is considered the surface energy, g, isgeneralised to: $\begin{matrix}{g = {\frac{K}{2L}{\pi \left( {g_{0} + g_{od} + g_{dd}} \right)}}} & (23)\end{matrix}$

[0096] where g₀, g_(od) and g_(dd) correspond to the surface energiesdue to the purely non-defect field, non-defect-defect field coupling anddefect-anti-defect field coupling, where: $\begin{matrix}{\quad {g_{o} \approx {\sum\limits_{i_{\max},j_{\min}}\left( {{\rho \quad i_{\max}} - {\rho \quad j_{\min}}} \right)}}\quad} & (24) \\{\quad {g_{od} = {\sum\limits_{\alpha}{m_{\alpha}{\rho \left( \lambda_{\alpha} \right)}}}}\quad} & (25) \\{g_{dd} = {\sum\limits_{\alpha,\beta}{m_{\alpha}m_{\beta}{\ln \left\lbrack {\sin^{2}\left( \frac{\lambda_{\alpha} - \lambda_{\beta}}{2} \right)} \right\rbrack}}}} & (26)\end{matrix}$

[0097] The equations above are only valid for${{\sum\limits_{\alpha}m_{\alpha}} = 0},$

[0098] otherwise g will increase linearly with the system height. Noticethat g_(o) and g_(dd) are always positive. Hence, the condition for thepossibility of the existence of multi-stable states is if:$\begin{matrix}{{g_{od} + g_{dd}} = {{\sum\limits_{\alpha}{m_{\alpha}\left\{ {{\rho \left( \lambda_{\alpha} \right)} + {\sum\limits_{\beta}{m_{\beta}\ln \quad {\sin^{2}\left( \frac{\lambda_{\alpha} - \lambda_{\beta}}{2} \right)}}}} \right\}}} \leq 0}} & (27)\end{matrix}$

[0099] for some combinatorial permutation of m's and λ's.

[0100] The director field configuration is given by: $\begin{matrix}{{\rho + {i\quad \theta}} = {{\ln \frac{w}{z}} + {\sum\limits_{\alpha}{m_{\alpha}\ln \quad {\sin \left( \frac{w - \lambda_{\alpha}}{2} \right)}}} + {i\quad \theta_{o}}}} & (28)\end{matrix}$

[0101] and the far from the surface alignment grating and liquid crystalinterface the surface behaviour of θ is: $\begin{matrix}{{\lim\limits_{v\rightarrow\infty}\theta} = {{- {\sum\limits_{\alpha}{m_{\alpha}\left( \frac{\lambda_{\alpha}}{2} \right)}}} + \theta_{o}}} & (29)\end{matrix}$

[0102] Under planar (zero twist) configuration and one elastic constantapproximation, the zero volt nematoelastic can be realised as the 2dimensional Laplace equation: $\begin{matrix}{{\frac{\partial^{2}\theta}{\partial x^{2}} + \frac{\partial^{2}\theta}{\partial y^{2}}} = 0} & (30)\end{matrix}$

[0103] where θ is the tilt angle of the nematic director field definedin the x-y plane. The problem is analogous to the two dimensionalelectrostatic, where θ is the electrostatic potential.

[0104] The solution to equation 30 is: $\begin{matrix}{{\theta (w)} = {{{Im}\quad {\ln \left( \frac{z}{w} \right)}} + \frac{\pi}{2}}} & (31)\end{matrix}$

[0105] where z=(x+iy) and w=(u+iv) are complex planes related by aconformal mapping such that z(w)=x(w)+iy(w) is the grating surfaceprofile when w=u+i0.

[0106] Solution 31 gives the homeotropic alignment at the gratingsurface: $\begin{matrix}\begin{matrix}{{\theta \left( {w = {u + {0i}}} \right)} = {{{Im}\quad {\ln \left( {\frac{x}{u} + {i\frac{y}{u}}} \right)}} + \frac{\pi}{2}}} \\{= {{\tan^{{- 1}\quad}\left( {\frac{y}{u}/\frac{x}{u}} \right)} + \frac{\pi}{2}}}\end{matrix} & (32)\end{matrix}$

[0107] The conformal mapping technique, z→ω, is required to be analyticin the upper half plane of ω for θ and hence the energy to benon-singular. Therefore,

lim_(84 →∞)w=cz  (33)

[0108] If c is real then: $\begin{matrix}{{\lim\limits_{v\rightarrow\infty}\theta} = {{{\lim\limits_{v\rightarrow\infty}{{Im}\left( \frac{z}{w} \right)}} + \frac{\pi}{2}} = \frac{\pi}{2}}} & (34)\end{matrix}$

[0109] From the solution of equation 31, one obtains the conjugatefunction, ρ, of θ which also satisfies the Laplace equation 30$\begin{matrix}{{\rho (w)} = {{{Re}\quad {\ln \left( \frac{z}{w} \right)}} = {\ln {\frac{z}{w}}}}} & (35)\end{matrix}$

[0110] ρ and θ can be understood as the analogues of the electric fieldintensity and potential in electrostatics. The lines of constants ρ andθ are orthogonal as electric lines and equipotentials are normal to oneanother. The mathematical meaning of ρ is the natural logarithm of theJacobian for the conformal transformation w→z, as described by M. RSpeigal, “Complex Variables”, Schaum's outline series, McGraw Hill,1974. Hence p measures, in the logarithmic scale, the magnitude of therate of change of z with respect to the rate of change of w. In otherwords, ρ₀ measures, in logarithmic scale, the ratio of an elementalarea, Δz, at z to its corresponding area, Δw, at w(z) under a conformaltransformation z⇄w. Hence ρ₀ evaluated at the concave parts of a surfaceis bigger than ρ₀ at the convex parts of the surface. FIG. 4 shows theconformal co-ordinates graphically; the bold lines (24) are the constant's and the normal lines (25) are the constant u's; points a (26), b (28)and c (30) represent the flat, convex and concave curvatures; ρ₀associate with these points are ordered as

ρ_(o)(c)>ρ₀(a)>ρ₀(b)

[0111] By means of a conformal transformation, Cauchy-Riemann conditionand change of integration variables, the deformation energy per unitsurface area per unit groove, g, can be expressed in the three differentways as follows: $\begin{matrix}{{g_{0} = {\frac{K}{2L}{\int{\int{{x}{y}\left\{ {\left( \frac{\partial\theta}{\partial x} \right)^{2} + \left( \frac{\partial\theta}{\partial y} \right)^{2}} \right\}}}}}}\quad} & \left( {36a} \right) \\{{= {\frac{K}{2L}{\int_{0}^{\infty}{{v}{\int_{0}^{L}{{u}\left\{ {{\frac{\partial\rho}{\partial u}\frac{\partial\theta}{\partial v}} - {\frac{\partial\rho}{\partial v}\frac{\partial\theta}{\partial u}}} \right\}}}}}}}\quad} & \left( {36b} \right) \\{{= {\frac{K}{2L}{\int{\int{{\rho}{\theta}}}}}}\quad} & \left( {36c} \right)\end{matrix}$

[0112] where L is the pitch of the groove of a given grating andK=K₁₁=K₂₂=K₃₃ is the elastic constant.

[0113] Point singularities can be added to the solution of equation 31without altering the boundary condition requirement of homeotropicsurface condition of equation 32. For a periodic grating surface, weconsider an array of singularities on the surface. Hence, the tiltangle, θ, of the director field becomes: $\begin{matrix}{\theta = {{{Im}\quad {\ln \left( \frac{z}{w} \right)}} + \frac{\pi}{2} + {{Im}\quad {\sum\limits_{\alpha}^{N}\quad {\sum\limits_{n = {- \infty}}^{\infty}\quad {m_{\alpha}{\ln \left( {w - \lambda_{\alpha} - {2\pi \quad n}} \right)}}}}}}} & (37)\end{matrix}$

[0114] where m_(α) and N are half integers representing the strength ofthe N nematic disclinations on a single groove of the grating surface,λ_(α) are N real numbers defined in the range [−π, π, ) representing thepositions (w=u+i0) of the m_(α) disclinations in the 0^(th) groove ofthe grating. In the transformed w plane, the periodicity of the grooveis conveniently scaled to 2π. The logarithmic functions in the summationin equation 37 are analogues of the well known functions for linecharges of strength m_(α) in two dimensional electrostatics.

[0115] Upon summing the infinite series in equation 37, on yields:$\begin{matrix}{{\rho + {i\quad \theta}} = {{\ln \frac{w}{z}} + {\sum\limits_{\alpha}^{N}{m_{\alpha}\ln \quad {\sin \left( \frac{w - \lambda_{\alpha}}{2} \right)}}} + {i\frac{\pi}{2}}}} & (38)\end{matrix}$

[0116] The deformation energy for θ given solution 38 is:$\begin{matrix}{g_{d} = {g_{o} + {\frac{\pi \quad k}{2\quad L}\left\{ {{\sum\limits_{\alpha}^{N}{m_{\alpha}{\rho \left( \lambda_{\alpha} \right)}}} + {\sum\limits_{\alpha,\beta}^{N}{m_{\alpha}m_{\beta}{\ln \left\lbrack {\sin^{2}\left( \frac{\lambda_{\alpha} - \lambda_{\beta}}{2} \right)} \right\rbrack}}}} \right\}}}} & (39)\end{matrix}$

[0117] The expression is valid for${\sum\limits_{\alpha}m_{\alpha}} = 0.$

[0118] Otherwise, g will increase linearly with the system height. Inthe second summation, λ_(α) − λ_(β)

[0119] is defined to be r when α=β. r<<L is the diameter of thedisclination cores.

[0120] The second summation in equation 38 is always positive. Thecondition for the possibilities of multi-stable states is given by:$\begin{matrix}{{{\sum\limits_{\alpha}^{N}{m_{\alpha}{\rho \left( \lambda_{\alpha} \right)}}} + {\sum\limits_{\alpha,\beta}^{N}{m_{\alpha}m_{\beta}{\ln \left\lbrack {\sin^{2}\left( \frac{\lambda_{\alpha} - \lambda_{\beta}}{2} \right)} \right\rbrack}}}} \leq 0} & (40)\end{matrix}$

[0121] for some configuration disclination lines on the grating positionat λ_(α)'s.

[0122] To minimise the first summation, the following criteria areobserved: $\begin{matrix}{\left. {m_{\alpha} > 0}\Leftrightarrow{\rho \left( \lambda_{\alpha} \right)} \right. = {\min\limits_{\lambda}\left( {\rho (\lambda)} \right)}} & \left( {41a} \right) \\{\left. {m_{\alpha} < 0}\Leftrightarrow{\rho \left( \lambda_{\alpha} \right)} \right. = {\max\limits_{\lambda}\left( {\rho (\lambda)} \right)}} & \left( {41b} \right)\end{matrix}$

[0123] It concludes that a positive indexed disclination (m_(α)>0) tendsto form at the position on a grating where the curvature is convex (ρ<c)and a negative index disclination (m_(α)<0) tends to form at theposition with a concave curvature (ρ>c).

[0124] For a given set of λ_(α)'s, the tilt angle of the director fieldat a distance far from the grating surface can be found from equation 38for θ by taking the limit of ν to infinity: $\begin{matrix}{{\lim_{v\rightarrow\infty}\theta} = {{- {\sum\limits_{\alpha}^{N}{m_{\alpha}\left( \frac{\lambda_{\alpha}}{2} \right)}}} + \frac{\pi}{2}}} & (42)\end{matrix}$

[0125] Implementation of this theory, allows the energy associated witha particular position of a pair of +½ and −½ defects, and the pretiltimparted to the liquid crystal at an infinite distance from the surface,to be calculated for an arbitrary grating shape. An arbitrary gratingshape is input into the model and the energy is calculated as a functionof both −½ defect position along the grating and +½ defect positionalong the grating. At points where the −½ defect is coincident with the−½ defect, the defects annihilate and the non-defect state is formed.

[0126]FIG. 5 shows a series of gratings and a representation of across-section through the energy profile. The energy profile is obtainedas a function of both −½ defect position and +½ defect position on thegrating, producing a three dimensional energy profile. FIG. 5b, 5 d, and5 f show a cross section of this profile (in each case the sameprofile).

[0127]FIG. 5a represents a symmetrical sinusoidal grating. It can beseen that two energy minima occur (30, 31). The first energy minimum(30) is associated with coincident −½ and +½ defect positions (i.e. thenon-defect state) has a calculated pretilt of 90°. The second energyminimum (31) is associated with the +½ defect being at the convex defectsite and the −½ defect being at the concave defect site; this gives apretilt of 0°.

[0128]FIG. 5c represents an asymmetric sinusoidal grating. It can beseen that two energy minima occur (33, 34). The first energy minimum(33) is associated with coincident −½ and +½ defect positions (i.e. thenon-defect state) has a calculated pretilt of 90°. The second energyminimum (34) is associated with the +½ defect being at the convex defectsite and the −½ defect being at the concave defect site; this gives apretilt of 36°. Hence, as found for the simple model above, anasymmetric grating with defect sites not fulfilling the criteria a=L/2produces a finite pretilt.

[0129]FIG. 5e represents an asymmetric square grating with four defectsites. It can be seen that five energy minima occur (35, 36, 37, 38,39). The energy minimum (37) is associated with coincident −½ and +½defect positions (i.e. the non-defect state) has a calculated pretilt of90°. The other four energy minima (35, 36, 38, 39) are associated withthe various combinations of +½ defect and −½ defect positions asdescribed with reference to 7. The energy minimum (39) gives a pretiltof 0°.

[0130] To summarise, it can be seen that a computer implementation ofthe above model allows the surface pretilt induced by a surfacealignment grating, and the energy associated with that particularconfiguration, to be calculated from a particular defect pair positionon a given surface alignment grating profile.

[0131] Multiple Zenithally Stable States and the Associated SurfacePretilt.

[0132] The model described above with reference to FIGS. 4 and 5demonstrates that for a given surface profile it is possible to obtain aplurality of stable surface states, and allows the pretilt associatedwith such states to be calculated. Such multi-stability is found withinone period of the grating when there are three or more defect sites andat least one defect site has a maximum curvature which is convex and atleast one defect site has a maximum radius of curvature which isconcave.

[0133] A plurality of defect sites per unit length of grating allows theformation of defect pairs at a plurality of positions within a singlegrating period. It is only possible for +½ and −½ defects to form inpairs; a single defect, or two −½ defects, can not form alone. Each +½and −½ defect pair position induces a liquid crystal pretilt that couldbe calculated rigorously using the model described with reference toFIGS. 4 and 5 above, or less rigorously using the simple model describedwith reference to FIGS. 1 to 3 above.

[0134] A plurality of defect sites per grating period, the formation ofdefect pair combinations and the pretilt associated with the variousdefect site configurations will now be described with reference to FIGS.6 to 9.

[0135]FIG. 6 depicts a surface alignment grating (40) with a single +½defect site (42) per grating period, L. The surface alignment gratinghas two possible −½ defect sites per grating period; a first −½ defectsite (44) and a second −½ defect site (46). Two possible defect statescould then be formed with a +½ defect at the +½ defect site (42) and a−½ defect at either the first −½ defect site (44) or the second −½defect site (46). These two possible defect pair configurations areshown in FIGS. 6a and 6b, where representative −½ defects (48) and +½defects (50) are also shown.

[0136] The symmetric grating of FIG. 6 can produce two possible pre-tiltangles θ₁=πd₁/L (for the configuration of FIG. 6a) and θ₂=πd₂/L (for theconfiguration of FIG. 6b), which are finite but symmetrical about thesubstrate normal. A non-defect configuration can also be adopted by thenematic liquid crystal at the grating surface. The surface alignmentgrating of FIG. 6 thus provides three (two defect and a non-defect)stable surface pretilt configurations.

[0137] Referring to FIG. 7, there exists on the surface alignmentgrating (52) a first +½ defect site (54), a second +½ defect site (56),a first −½ defect site (58) and a second −½ defect site (60). Liquidcrystal (2) in contact with the surface alignment grating (52) couldadopt any one of four possible defect configurations, as shown in FIGS.7a, 7 b, 7 c and 7 d. The defect pair configurations shown in FIGS. 7a,7 b, 7 c and 7 d will induce surface pretilts of θ₁, θ₂, θ₃ and θ₄respectively. The surface pretilt angles θ₁, θ₂, θ₃ and θ₄ can beestimated using equation 17 from the ratios of distances d₁, d₂, d₃, d₄to L.

[0138] or a symmetric grating of the type shown in FIG. 7, the surfacepretilt angles θ₁ and θ₂ occupy angles which are complimentary, and aretherefore symmetric about the substrate normal. The same is true for θ₃and θ₄. In practice the θ₁ and θ₂ states have the lower energyconfiguration since the high average surface tilt possessed by θ₃ and θ₄can be more readily attained by adopting the non-defect high tiltconfiguration. Equivalent but opposite pretilts may also haveadvantages, such as wider viewing angle (similar to dual domain TN).

[0139] Referring to FIG. 8, it is possible for a symmetric or anasymmetric grating to have a surface profile such that a certaincombination, or certain combinations, of +½ defect sites and −½ defectsites will fulfil the zero pretilt criteria of equation 17 thusproducing one or more defect states of zero surface pretilt (i.e.d=L/2).

[0140]FIG. 8a shows a symmetric alignment grating (62) which has fourdefect sites per unit length; a first −½defect site (64), a second −½defect site (66), a first +½ defect site (68) and a second +½ defectsite (70). If a −½ defect forms at the first −½ defect site (64) and a+½ defect forms at the first +½ defect site (68), the criteria L=2d isfulfilled and the defect state will impart a zero pretilt to the liquidcrystal (2) in contact with the grating surface (62). Similarly, zeropretilt is imparted to the liquid crystal (2) by the surface alignmentgrating (62) if a −½ defect forms at the second −½ defect site (66) anda +½ defect forms at the second +½ defect site (70). The two otherpossible combinations of the −½ and +½ defect position will impart anon-zero surface pretilt to the liquid crystal layer (2) according toequation 17.

[0141]FIG. 8b shows an asymmetric alignment grating (72) which has fourdefect sites per unit length; a first −½ defect site (74), a second −½defect site (76), a first +½ defect site (78) and a second +defect site(80). If a −½ defect forms at the second −½ defect site (76) and a +½defect forms at the second +½ defect site (80), the criteria L=2d isfulfilled and, when this particular defect state is formed, the gratingsurface (72) imparts a zero pretilt to the liquid crystal (2). The threeother possible combinations of the −½ and +½ defect position will imparta non-zero surface pretilt to the liquid crystal layer (2) according toequation 17. Note that although there are four defect sites in thisexample, they alternate convex, convex, concave, concave and thereforean additional defect pair cannot be created.

[0142] Each of the five possible states that may form on the symmetricalignment grating of FIG. 8a, or the asymmetric grating of FIG. 8b, willinduce a certain liquid crystal surface pretilt angle and will havecorrespondingly different energies. The lower energy configurations willbe those which induce the lower pretilt angles. If an asymmetric gratingwas so profiled, with an appropriate groove depth and pitch, the energyof one or more of the defect states could be made such that those defectstates are less energetically favourable than the non-defect state andsome or all of the other defect states.

[0143] Surface grating structures can be designed, using the models andexamples described above, where the defect sites are positioned so as toinduce a plurality of states of various different energies, and/or wherethe surface pretilt of one or more of the defect states is to becontrolled (for example to get defect states which induces substantiallyzero pretilt).

[0144] The construction of multi-faceted gratings is limited only by thefabrication process. However it is unlikely that a grating with morethan approximately 10 defect sites per grating period would be required.FIG. 9 shows an alignment grating (82) with four −½ defect sites (84,86, 88, 90) per unit length and four +½ defect sites (92, 94, 96, 98)per unit length. In addition to the non-defect (homeotropic) state, thealignment grating structure (82) would enable sixteen defect stateconfigurations to be formed. No more than one pair of defect can form adefect state on this surface; to do so requires alternating +½ and −½defect sites. The surface pretilt imparted to the liquid crystal by eachof the defect states is defined by equation 17, and could also becalculated using the more rigorous model described above with referenceto FIGS. 4 and 5.

[0145] Surface alignment gratings may be profiled so as to favour theformation of more than one pair of +{fraction (1/2)} and −½ defects perunit length of grating, by producing structures with alternating +½ and−½ defect sites.

[0146] An example of a surface alignment grating, profiled so as tofavour the formation of more than one pair of +½ and −½ defects per unitlength of grating, will now be described with reference to FIG. 10. Thealignment imparted to a nematic liquid crystal layer by the type ofgrating structures described with reference to FIG. 10 will then bedescribed with reference to FIGS. 11 to 12.

[0147] A blazed surface alignment grating (100) of pitch P and amplitudeA is shown in FIG. 10a, and may be described by the function:$\begin{matrix}{{y(x)} = {{f\quad {{n1}(x)}} = {\frac{A}{2}{\sin \left( {\frac{2\quad \pi \quad x}{p} + {\delta \quad {\sin \left( \frac{2\quad \pi \quad x}{p} \right)}}} \right)}}}} & (43)\end{matrix}$

[0148] where:

[0149] A=half of the peak to peak amplitude of the grooves

[0150] p=period or pitch of the grooves

[0151] δ=the asymmetry of the function (δ=0 gives a sinusoidal functionand δ>0 gives a blazed asymmetric profile).

[0152] Within an overall period p, it is possible to have two or moresub-periods which are, for example, of pitch p₁ and p₂ and of amplitudeA₁ and A₂. Such surface profiles will now be described for thesinusoidal function ƒn1(x), described by equation 43 above, withreference to FIGS. 10b to 10 d. The technique of building up an overallsurface alignment grating of period p from two smaller sub-units of asmaller pitch and/or of different amplitudes is not restricted tosinusoidal functions of the form described herein but may also beapplied to a plurality of sub-units provided that the condition p₁+p₂ .. . +p_(n)=p is met.

[0153]FIG. 10b shows a surface alignment grating (102) made up of onesub-period of ƒn1(x) (given in equation 43) with pitch p₁ and amplitudeA, plus one sub-period of ƒn1(x) with pitch p₂ and amplitude A, suchthat p=p₁+p₂. In FIG. 10b, p₂>p₁. FIG. 10c shows a surface alignmentgrating (103) profiled such that one period p of the grooved surface ismade up of one sub-period of the function ƒn1(x) with pitch p/2 andamplitude A₁ plus one sub-period of the function ƒn1(x) with pitch p/2and amplitude A₂. FIG. 10d shows a surface alignment grating (120)profiled such that one period p of the grooved surface is made up of oneperiod of the function ƒn1(x) with pitch p₁ and amplitude A₁ plus oneperiod of the function ƒn1(x) with pitch p₂ and amplitude A₂.

[0154] The surface alignment grating structure (102) given in FIG. 10b,when in contact with a nematic liquid crystal (2) is depicted in FIG.11. The nematic liquid crystal director, n, is perpendicular to theiso-contour lines (101). From FIG. 11, it can be seen that the surfacealignment grating structure (102) has a first (104) and second (106) +½defect site and a first (108) and second (110) −½ defect site. Anon-defect, homeotropic, state is depicted in FIG. 11a.

[0155] In FIG. 11b, a +½ defect (112) forms at the first +½ defect site(104) and a −½ defect (114) forms at the first −½ defect site (108),giving an intermediate pretilt state governed by the relative positionof the defect pair according to equation 17 as described above.

[0156] In FIG. 11c, a +½ defect (112) forms at the first +½ defect site(104) and a −½ defect (114) forms at the first −½ defect site (108) andin addition a second +½ defect (116) forms at the second +½ defect site(106) and a second −½ defect (118) forms at second −½ defect site (110).The formation of the two defect pairs per unit length of grating willproduce a low surface pretilt state wherein the pretilt adopted by theliquid crystal a short distance, compared with the cell gap, from thegrating surface (102) will be the average of that expected (fromequation 17 above) for the defect states of a grating of pitch pi and agrating of pitch p₂. The different grating profiles of the portion ofthe grating of pitch p₁ and the portion of the grating of pitch p₂causes the first and second defect pairs to have different energiesassociated with their formation. The energy associated with a defectpair on a grating surface can be calculated using the detailed model ofgrating induced surface pretilt described above with reference to FIGS.4 and 5. Qualitatively, it can be seen that the different groove depth(A) to pitch (p) ratio of the two sub-components of the surfacealignment grating (102) will be different, and consequently that theenergy associated with the formation of defect pairs on the twosub-components of the surface alignment grating (102) will also differ.

[0157] In summary, it can be seen from FIG. 11 that there are threepossible configurations, each producing a different surface pretiltangle, that are adopted when two pairs of defects form on twosub-periods of a grating; namely a non-defect, a single defect pairstate and a dual defect pair state. The single defect pair state couldgive rise to other variants, but these are less likely to occur becausethe energy of formation associated with sharp facets is significantlydifferent to that associated with the shallower facets.

[0158] The surface alignment grating structure (120) given in FIG. 10d,when in contact with a nematic liquid crystal (2) is depicted in FIG.12. Referring to FIG. 12, it can be seen that a similar behaviour tothat described with reference to FIG. 11 is obtained with a surfacealignment grating (120) of an overall period p that consists of twosub-periods p₁ and p₂ with corresponding amplitudes A₁ and A₂. Thesurface alignment grating (120) has a first (122) and second (124) +½defect site and a first (126) and second (128) −½ defect site. Anon-defect, homeotropic, state is depicted in FIG. 12a.

[0159] From FIG. 12b a defect state is shown where a first +½ defect(130) forms at the first +½ defect site (122) and a first −½ defect(132) forms at the first −½ defect site (126), giving an intermediatepretilt state governed by the relative position of the defect pairaccording to equation 17 as described above. FIG. 12c depicts a defectstate wherein two defect pairs have formed; a first +½ defect (130) atthe first +½ defect site (122), a first −½ defect (132) at the first −½defect site (126), a second +½ defect (134) at the second +½ defect site(124) and a second −½ defect (136) at the second −½ defect site (128).As described with reference to FIG. 11 above, the pretilt associatedwith the defect state of FIG. 12b is governed by equation 17 whereas thepretilt associated with the defect pair state of FIG. 12c can becalculated by determining the average pretilt of two gratings of pitchesp₁ and p₂. The energy associated with each defect pair can, as describedwith reference to FIG. 11 above, be determined using the model describedherein with reference to FIG. 4 and 5.

[0160] To summarise, the surface alignment grating of period P describedwith reference to FIG. 12 above contains two distinct sub-periodregions. The difference in defect energy associated with each of thesub-periods means that it is possible for stable states to form with nodefects, one defect pair or two defect pairs. Each of these states willproduce a different surface pretilt, allowing a tri-stable device to bereadily constructed from such a surface alignment grating

[0161] As described above with reference to FIG. 10 to 12, a gratingconsist of a number of sub-periods. It is also possible for eachsub-period to possess more than two defects sites, thereby combining thestructures described in FIGS. 6 to 9 in the manner described withrespect to FIGS. 10 to 12.

[0162] To achieve multi-stability, i.e. a surface alignment gratingwhich imparts three or more stable pretilt angles in the same azimuthalplane to the liquid crystal in the vicinity of the surface, when morethan one pair of defects form per unit length of grating requires theoverall grating period p to be less that half of the gap between theupper and lower cell walls. If the overall pitch p is more thanapproximately half the cell gap, defect pairs associated with adjacentsub-unit grating periods contained within the overall grating periodwill induce a surface pretilt that does not, in the vicinity of thesurface, combine so as to form a plurality of stable pretilt angles inthe same azimuthal plane. If the overall pitch p is more thanapproximately half the cell gap and, for example, two defect pairs pergrating period could form, the surface pretilt associated with eachdefect pair would not merge within a short distance of the surface butwould produce two distinct and adjacent regions of different bulk liquidcrystal configuration (i.e. a striped texture when observed optically).

[0163] Although achieving a uniform pretilt within a short distance ofthe surface alignment grating, thereby ensuring that a uniform opticaltexture is attained, is ideal the formation of adjacent regions ofdifferent bulk liquid crystal configuration (thus adjacent regions ofdifferent optical appearance) is perfectly acceptable for displayapplications provided that the size of such regions is sufficientlysmall so that the separate regions can not be readily perceived bydisplay observers.

[0164] Device Configurations.

[0165] A person skilled in the art would be aware of numerous deviceconfigurations which would allow the multi-stable surface describedherein to be exploited. Several of the possible liquid crystal cell anddevice configurations will now be described with reference to FIG. 13.

[0166] One cell configuration which allows the existence of a pluralityof stable surface pre-tilt states to be exploited as a plurality ofgreyscale levels is shown in cross section in a stylised form in FIG.13. The cell is constructed from two cell walls (140,142), where thefirst cell wall (142) has a multi-stable surface alignment grating (144)formed on its internal surface, in this example a tri-stable surfacealignment grating in accordance with the teaching described above,whilst the second cell wall (142) has is treated so as to inducehometropic alignment to the nematic liquid crystal (2).

[0167] The first (142) and second (140) cell walls are maintainedtypically 1-10 μm apart by a spacer ring (not shown), numerous beads ofthe same dimension dispersed within the liquid crystal (not shown) ornumerous beads of the same dimension dispersed within any glue used tobond the cell walls together (not shown). Many other techniques ofmaintaining a gap between the cell walls are readily known to a personskilled in the art.

[0168] A nematic liquid crystal (2) sandwiched between the first (142)and second (140) cell walls of can exist in any of three stableconfigurations; the non-defect configuration shown in FIG. 13(a), thedefect configuration shown in FIG. 13(b) or the defect configurationshown in FIG. 13(c). The two defect state configurations of FIGS. 13(a)and 13(b) arising from two possible positions which the bend defect canadopt on a the tri-stable surface alignment grating (144). For manynematic materials, a splay or bend deformation will lead to amacroscopic flexoelectric polarisation which is represented by thevector P in FIG. 13(b) and P′ in FIG. 13(c). A dc pulse applied to theelectrodes (146) can couple to this flexoelectric polarisation, which ispredominantly close to the alignment surface, and depending on its signand magnitude any one of the three configurations can be selected.

[0169] The cell configuration used to exploit the existence of atri-stable surface alignment grating, described with reference to FIG.13 above, will also allow multi-stable surface alignment gratings to beexploited as multi-stable devices. Maximum contrast will be achieved ifone of the defect states adopts a zero pretilt configuration by havingdefects positioned so as to fulfil the criteria a=L/2.

[0170] To obtain a display device with optical contrast, the cellconfigurations described above can be combined with externalpolariser(s) and/or a reflector and the device may be operated in eithertransmissive or reflective mode. Alternatively, a dichroic dye may bemixed with the liquid crystal to get different absorption of light inthe various multi-stable configurations. All these techniques ofproducing optical contrast from liquid crystal cell configuration arewell known to a person skilled in the art.

[0171] Optical compensation techniques, which would be well known toperson skilled in the art, may also be employed to enhance the opticalcontrast and viewing angle characteristics of any of the plurality ofdefect states.

[0172] Any nematic material with positive, negative or zero dielectricanisotropy may be used in the cell configuration. Dual frequency nematicmaterials, where the sign of dielectric anisotropy changes with thefrequency of applied voltage, may also be used. In a preferredembodiment a high positive dielectric anisotropy, and associated highflexoelectric coefficient, may be used. Super-twist nematic and activematrix nematic materials would be suitable, although there is norequirement for the high ionic purity of liquid crystal required for theoperation of active matrix devices.

[0173] The cell walls may be formed of a relatively thick non flexiblematerial such as a glass, or one or both walls may be formed of aflexible material such as a thin layer of glass or a plastic flexiblematerial e.g. polyolefin or polypropylene. A plastic cell wall may beembossed on its inner surface to provide a grating. Additionally, theembossing may provide small pillars (e.g. of 1-10 μm height and 5-50 μmor more width) for assisting in correct spacing apart of the cell wallsand also for a barrier to liquid crystal material flow when the cell isflexed. Alternatively the pillars may be formed by the material of thealignment layers.

[0174] The grating may be a profiled layer of a photopolymer formed by aphotolithographic process e.g. M C Huntly, Diffraction Gratings(Academic Press, London, 1982) p 95-125; and F Horn, Physics World, 33(March 1993). Alternatively, the grating may be formed by embossing; M TGale, J Kane and K Knop, J App. Photo Eng, 4, 2, 41 (1978), or ruling; EG Loewen and R S Wiley, Proc SPIE, 88 (1987), or by transfer from acarrier layer. A grating of 0.2 μm to 5 μm pitch, with a groove depth ofbetween 0.1 μm to 3 μm is preferred.

[0175] Experimental examples, to backup the theoretical analysisdescribed above, will now be described with reference to FIGS. 14 to 22.

EXAMPLE 1

[0176] It will now be shown, with reference to FIGS. 14, how asymmetrical grating structure with only one pair of defect sites pergrating unit length induces a liquid crystal surface pretilt ofapproximately zero degrees.

[0177] A solution comprising 4 parts 1813 Shipley photoresist to onepart PGMEA thinners was spun onto an Indium Tin Oxide (ITO) coatedsubstrate producing a photoresist film thickness of approximately 0.8μm. Holographic interference of two beams was used to create a gratingof 500 nm pitch with a profile very close to being sinusoidal. Thesubstrate was then developed to reveal the grating structure which wasthen hardened by exposure to light from a high intensity 254 nm lightsource, followed by a hard-bake at 180° C. which rendered the gratinginsoluble in liquid crystal material. The grating used for theexperiment above was analysed, after performing the above experiments,using cross-sectional SEM and the grating profile is shown in FIG. 14.

[0178] The grating was treated with a homeotropic surfactant andassembled into a 10 μm cell opposite a planar anchoring grating whichhad been made by photolithography. After filling with liquid crystal andcooling into the nematic phase, only one state was observed. Nodegeneracy was present in this cell which immediately suggests a pretiltof zero. The pretilt of the bistable grating surface was measured, usingthe rotating crystal method to be 0.2°.

EXAMPLE 2

[0179] It will now be shown, with reference to FIGS. 15 and 16, how asymmetrical grating structure with two +½ defect sites and one −½ defectsite per grating unit length will induces two liquid crystal defectconfigurations with surface pretilts significantly greater than zerodegrees.

[0180] A solution comprising 4 parts 1813 Shipley photoresist to onepart PGMEA thinners was spun onto an ITO coated substrate producing aphotoresist film thickness of approximately 0.8 μm. A 1 μm pitchchrome-on-glass master-grating was bolted down so that it sat inintimate contact with the photoresist coated substrate. The assembly wasexposed at normal incidence to a well-collimated beam of light from ahigh power mercury lamp. A variable neutral density filter was putbetween the light source and the master grating so that a variableexposure was made in the direction of the grating grooves. The substratewas then unclamped and developed to reveal a grating structure which wasthen hardened by exposure to light from an high intensity 254 nm source,followed by a hard-bake at 180° C. which rendered the grating insolublein liquid crystal material. A homeotropic surface treatment was applied.A grating made in this way which exhibited similar tilt angles in thelow tilt configuration was snapped along the direction perpendicular tothe grating grooves and characterised using SEM. The resultingphotograph shown in FIG. 15 is a cross section of the grating profile.

[0181] This symmetrical grating with normal boundary conditions wasassembled opposite a second symmetrical grating which had been madeusing an identical method, but which was not given the homeotropicanchoring treatment or the variable exposure. The grating grooves wereassembled perpendicular to each other with a cell spacing ofapproximately 10 μm. The cell was capillary-filled with liquid crystaland on cooling from the isotropic phase adopted an alignmentconfiguration along the grating grooves of the planar anchored grating.The configuration at the surface alignment grating surface wasdetermined by the depth of the grating which resulted from the variableexposure.

[0182] At the shallow end of the surface alignment grating a degeneratehybrid aligned configuration was realised which corresponded toformation of the high surface tilt non-defect state. However most of thecell took up low tilt configurations, which were highly degenerate withtilt disclination lines between two states of equal birefringence. Themere presence of this degeneracy confirms that some surface tilt isobtained from the surface alignment grating since there is no mechanismfor the existence of surface tilt on the planar grating.

[0183] To measure the surface pretilt of one of the two stable defectstates, the cell was heated to the isotropic phase and then cooled undera magnetic field which allowed a monodomain possessing only one sign oftilt to form. The average bulk tilt was measured in the cell using therotating crystal method, and the results obtained were doubled to givethe surface tilt on the surface alignment grating. The measured tiltangle, as a function of grating exposure intensity (and hence groovedepth), are given in FIG. 16. A pretilt substantially greater than zerois observed for this symmetric grating, as would be predicted from themodels described above.

EXAMPLE 3

[0184] As described herein, it is possible for particular grating groovedesigns to allow two different liquid crystal alignment configurationswhich contain defects as well as the non-defect state. An example ofsuch a tri-stable surface is now described with reference to FIGS. 17and 18.

[0185] The grating surface was fabricated as follows. Photoresist(Shipley 1805) was spun onto a glass substrate which already containedan Indium Tin Oxide overlayer. Spinning was carried out for 30 secondsat 3000 rpm followed by a 10 minute softbake at 100° C. Next the samplewas exposed to UV radiation (250 mJ/cm², 360-440 nm, incident 60° fromthe sample normal) with the mask in hard contact with the sample. Theresist image was developed using Shipley M319 for 10 seconds followingby a water rinse. Next the grating pattern was hardened by exposing todeep UV (7.5 J/cm², 254 nm) and then baking at 180° C. for 2 hours.Finally the grating surface was processed in order to induce homeotropicalignment of the LC and a 4 μm thick cell was constructed whichconsisted of one grating surface and one flat surface designed to givehomeotropic alignment of the LC. The cell was filled with a nematicliquid crystal material. FIG. 17 shows an SEM image of a grating made bythis method. A high degree of asymmetry is observed due to the off-axisUV illumination.

[0186] Application of appropriate pulses to the cell was found to leadto three different states which are labelled ND, D1 and D2. FIG. 18shows the schematic bulk liquid crystal (2) configuration of each ofthese states. A bipolar pulse (0.98 ms duration) with a negativetrailing part was found to select the ND state when the amplitude wasabove 8.8 V (polarity defined with respect to the grating surface).Bipolar pulses with a positive trailing part selected the D1 state above11.9 V and the D2 state above 22.0 V.

[0187] The relative optical transmission of the three states was alsomeasured with the cell between crossed polarisers oriented at ±45° tothe grating grooves. It was found that the ND state transmission (Arb.Units) was 0.008, the D1 transmission was 0.103 (Arb. Units) and the D2transmission was 0.497 (Arb. Units). In this example the intermediate D1state has a brightness of about 20% of the D2 state. The relativebrightnesses of the states can be adjusted by using different gratingfabrication parameters (exposure time , exposure angle , developmenttime) to vary the profile of the grating surface.

EXAMPLE 4

[0188] As described above with reference to FIGS. 10 to 12, a grating ofoverall period p may be constructed from two sub-gratings of period p₁and p₂ where P₁+p₂=p. A method of manufacturing such gratings, whichallow a multi-stable device to be constructed, will now be describedwith reference to FIGS. 19 to 22

[0189] A grating mask which has alternating chrome lines (or gaps) canbe used to produce a surface alignment grating with alternating groovespacing; as shown in FIG. 19.

[0190]FIG. 19a depicts a chrome mask with constant clear gaps of 0.5 μm(154) and alternate chrome lines of 0.5 μm (150) and 0.6 μm (152);termed an alternating chrome mask (148). FIG. 19b depicts a chrome maskwith constant chrome lines of 0.5 μm (150) and alternate clear gaps of0.5 μm (154) and 0.6 μm (156); termed an alternating gap mask (149).

[0191] A surface alignment grating has been fabricated using thealternating gap mask (149) of FIG. 19b. The following method was used tofabricate this device. Photoresist (Shipley 1813) was spun onto a glasssubstrate which already contained an Indium Tin Oxide overlayer.Spinning was carried out for 30 seconds at 4000 rpm followed by a 10minute softbake at 100° C. Next the sample was exposed to UV radiation(150 mJ/cm², 360-440 nm, incident 8° from the sample normal) with thealternating gap mask (149) in hard contact with the sample.

[0192] The resist image was developed using Shipley MF319 for 10 secondsfollowing by a water rinse. Next the grating pattern was hardened byexposing to deep UV (6 J/cm², 254 nm) and then baking at 180° C. for 2hours. Finally the grating surface was post processed in order to inducehomeotropic alignment of the liquid crystal and a 4 μm thick cell wasconstructed which consisted of one grating surface and one flat surfacedesigned to give homeotropic alignment of the liquid crystal.

[0193] The cell was filled with a nematic liquid crystal material. FIG.20 shows an SEM profile of a grating produced by this method.Examination of this image shows that the distance between the groovepeaks alternates between 1.0 μm and 1.1 μm as defined by thephotolithographic mask

[0194] Three possible stable states of the liquid crystal cell wereobserved; the entire grating surface in the non-defect (ND) state, asingle pair of defects forming per grating unit length (the D1 state)and two pairs of defects forming per unit length (the D2 state) With theoptimum pulses, the D1 state was obtained uniformly across the entiresample. The ND state is selected by a bipolar waveform with a negativetrailing pulse (applied to the grating surface) while the D1 and D2states are selected by a bipolar waveform with a positive trailingpulse.

[0195]FIG. 21 shows the transmission of this cell after bipolar pulsesof various voltages. In this case the bipolar pulse width was 0.98 ms.The curve clearly shows an intermediate level which is stabilised acrossa voltage range of about 1.5 V. In this case the transmission of the D1state is 31% of the full D2 state but this level can be controlled bycareful adjustment of grating design or the cell geometry.

[0196] Examination of the cell using polarised optical microscopy showedthat the D1 state actually consisted of two regions of distinct bulkliquid crystal alignment. The two distinct alignment regions correspondto variations in liquid crystal alignment (because of the formation ofthe first defect pair at one pair of defect sites and the existence ofno defect pair at the second pair of defect sites) between the twosub-gratings of 1.1 μm and 1.0 μm pitch. Increasing the cell gap, orreducing the grating pitch, would cause the variation of liquid crystalaccross the grating surface to merge within a shorter distance from thegrating surface reducing the variations in bulk liquid crystal alignmentthat were observed in this case. However, the existence of a stripedtexture on a microscopic scale is irrelevant when considering displayapplications because such variations can not be perceived by the displayobserver; only multiple grey-levels are observed.

[0197]FIG. 22 shows the switching thresholds of the three states (ND, D1and D2) as a function of pulse width. The three curves show the noswitch (first speckle) voltage, the voltage for the full D1 state andfinally the voltage for full switching. The curves remain parallelacross a wide frequency range. In this case the partial switch widthfrom ND to D1 is 7.6% while from D1 to D2 it is 8.8%.

[0198] It was noted for this cell that the D2 state was not obtained forpulses longer than 1ms (half width). For a 2 ms pulse, a complete D1state was obtained across the voltage range of 31.2-56.1 volts abovewhich some over-switching occurred. This provides an additional method(pulse width modulation) of accurately selecting the D1 state.

[0199] Referring to FIG. 23, additional advantages of obtaininggreyscale using a multi-stable device of the present invention, ratherthan relying on the prior art techniques, become apparent.

[0200]FIG. 23a shows the typical optical transmission versus appliedelectrical energy characteristics of a bistable device; hereinafter theterm electrical energy means the duration of the switching pulsemultiplied by its voltage. The first curve (200) represents the energyversus optical transmission characteristics for switching condition 1and the second curve (202) represents the energy versus transmissioncharacteristics for switching condition 2. The switching conditions 1and 2 are representative of the different switching conditions, orproperties, that are typically found at different points across adevice. The existence of different switching conditions across a deviceis known in the prior art and may arise for many reasons; for examplevariations in temperature, cell gap, alignment or driver circuitry.

[0201] Analogue (or domain) grey-scale techniques are known in the priorart and are described in the introduction above. Known domain grey-scaletechniques involve partially switching some domains, so that differentgrey-levels can be formed by varying the number and/or size of thedomains in that pixel. If the desired grey-level is, say, 50%transmission then a pulse of τV₁ will produce the desired transmissionlevel (i.e. level T1 in FIG. 23a) for switching condition 1. The use ofan energy pulse τV₁ for areas with the switching condition 2 willproduce a significantly difference transmission (level T2 in FIG. 23a).The variation of transmission (i.e. ΔT) is significant for small changesof the relative conditions because the partial switching width isusually rather narrow whilst the transmission versus applied electricenergy characteristic is steep. This makes domain grey-scale verydifficult to implement practically.

[0202] Referring to FIG. 23b, the optical transmission versus appliedelectrical energy characteristics of a prior art multiple thresholddevice is shown. Each pixel of a multiple threshold device issub-divided into two or more areas, for example an area A and an area B.The bistable liquid crystal will respond differently applied electricalenergy in each of the sub-divided pixels area because of someappropriate treatment; such as holes in electrodes, passive dielectriclayers etc. Again, different switching conditions are typically presentacross such a device, and condition 1 is represented by the first curve(204) and condition 2 is represented by the second curve (206).

[0203] To achieve a linear grey-scale characteristic, areas A and B ofeach pixel would be of equal area so that when the electrical energy issufficient to switch one area (e.g. τV₁ is applied) the resultanttransmission of the pixel is 50%. In such a device, the transmission isinsensitive to whether switching condition 1 or switching condition 2 ispresent in areas A and B. Multiple threshold techniques overcome thesensitivity to switching condition present with analogue grey-scaletechniques of the type described with reference to FIG. 23a above, butdividing each pixel into areas with different switching characteristicsadds substantial extra cost and complexity to the device. Moreover, itlowers the effective resolution of the device and can lead to unwantedimage artefacts for certain image patterns.

[0204] Referring to FIG. 23c, the optical transmission versus appliedelectrical energy characteristics of a tri-stable device is shownschematically. As described above, the liquid crystal may adopt a firststable configuration and provide a dark state transmission level (213),it may adopt a second stable configuration and provide an intermediatestate transmission level (214) or it may adopt a third stableconfiguration and provide a light state transmission level (215). Aswith bistable devices, different switching conditions may be present inthe device; for example switching condition 1 is represented by thefirst curve (210) and switching condition 2 is represented by the secondcurve (212).

[0205] To achieve a linear grey-scale characteristic, the second stableconfiguration of the tri-stable device described with reference to FIG.23c is adapted such that it provides a 50% transmission level. It can beseen that the 50% transmission level can be selected by the applicationof suitable electrical energy such as τV₁. In this device, thetransmission selection is insensitive to whether switching condition 1or switching condition 2 is present in the particular pixel. As with theprior art method of using multiple thresholds, the use of three or morestable liquid crystal configuration removes greyscale errors associatedwith variations across the panel. However, using a device having threeor more stable liquid crystal configuration avoids the cost associatedwith sub-pixellation and does not suffer from reduced resolution or thepresence of spatial artefacts inherent in multiple threshold devices.

1. A liquid crystal device capable of adopting at least two stablestates comprising a layer of liquid crystal material located between twocell walls, a means of applying a voltage to the liquid crystal layerand a surface alignment grating on the internal surface of at least onecell wall wherein the surface profile of the surface alignment gratingcomprises three or more defect sites per grating period with at leastone +½ defect site per grating period and at least one −½ defect siteper grating period so that that the liquid crystal molecules can adoptany one of two or more stable pretilt angles in the same azimuthal planein the locality of the surface and wherein the liquid crystal device isarranged such that two or more stable liquid crystal molecularconfigurations can exist and wherein application of a suitable voltagecauses the liquid crystal to adopt any one of two or more stableconfigurations.
 2. A liquid crystal device of claim 1 wherein the liquidcrystal molecules can adopt any one of three or more stable pretiltangles in the same azimuthal plane in the locality of the surface andwherein the arrangement is such that three or more stable liquid crystalmolecular configurations can exist and wherein application of a suitablevoltage causes the liquid crystal to adopt any one of three or morestable configurations.
 3. A liquid crystal device as claimed in claim 1wherein one pair of +½ and −½ defect sites are situated so as to imparta low surface pretilt for one defect state.
 4. A liquid crystal deviceas claimed in claim 3 wherein the low surface pretilt state is of asignificantly lower energy than that of any of the other possible defectstates wherein only the non-defect state and the defect state of lowpretilt can be readily selected on application of a voltage.
 5. A liquidcrystal device as claimed in claim 1 wherein the surface alignmentgrating structure is treated with a material that induces a homeotropicalignment of the liquid crystal director with respect to the localsurface direction.
 6. A liquid crystal device as claimed in claim 1wherein the surface alignment grating structure is formed from amaterial that induces a homeotropic alignment of the liquid crystaldirector with respect to the local surface direction.
 7. A liquidcrystal device as claimed in claim 1 wherein the surface alignmentgrating structure is treated with a material that induces planaralignment of the liquid crystal director with respect to the localsurface direction.
 8. A liquid crystal device as claimed in claim 1wherein the surface alignment grating structure is formed from amaterial that induces planar alignment of the liquid crystal directorwith respect to the local surface direction.
 9. A liquid crystal deviceas claimed in claim 1 wherein the liquid crystal material is a nematicliquid crystal material.
 10. A liquid crystal device as claimed in claim9 wherein the nematic liquid crystal material has a positive dielectricanisotropy.
 11. A liquid crystal device as claimed in claim 7 whereinthe liquid crystal material is a nematic liquid crystal material.
 12. Aliquid crystal device as claimed in claim 11 wherein the nematic liquidcrystal material has a negative dielectric anisotropy.
 13. A liquidcrystal device as claimed in claim 1 wherein one cell wall has a surfacealignment grating structure and the other cell wall has a surface whichinduces homeotropic alignment of the liquid crystal.
 14. A liquidcrystal device as claimed in claim 1 wherein one cell wall has a surfacealignment grating structure and the other cell wall has a surface whichinduces planar homogenous alignment of the liquid crystal.
 15. A liquidcrystal device as claimed in claim 1 wherein both cell walls havesurface alignment grating structures.
 16. A liquid crystal device asclaimed in claim 1 wherein the pitch of the surface alignment gratingstructure is greater than 500 nm.
 17. A liquid crystal device as claimedin claim 1 wherein the pitch of the surface alignment grating structureis greater than 800 nm
 18. A liquid crystal device as claimed in claim 1wherein the pitch of the surface alignment grating structure is greaterthan 1 μm.
 19. A liquid crystal device as claimed in claim 1 wherein thepitch of the surface alignment grating structure is less than 5 μm. 20.A liquid crystal device as claimed in claim 1 wherein the pitch of thesurface alignment grating structure is less than 2 μm.
 21. A liquidcrystal device as claimed in claim 1 wherein the groove depth of thesurface alignment grating structure is within the range of 0.1 μm to 3μm.
 22. A liquid crystal device as claimed in claim 1 wherein the twocell walls are separated by between 1-20 μm.
 23. A liquid crystal deviceas claimed in claim 1 wherein the means of applying a plurality ofvoltages to the liquid crystal layer comprises a layer of electricallyconductive, and substantially optically transparent, material applied tothe internal surface of both cell walls.
 24. A liquid crystal device asclaimed in claim 15 wherein the layers of electrically conductivematerial are applied to the internal surface of both cell walls and arepatterned so as to produce an array of addressable pixels.
 25. A liquidcrystal display comprising the liquid crystal device as claimed in claim1 and further comprising a means for optically distinguishing between atleast two of the stable liquid crystal configurations adopted.
 26. Aliquid crystal display as claimed in claim 25 wherein the means foroptically distinguishing between at least two of the liquid crystalconfigurations adopted comprises a pair of polarisers placed one eitherside of the liquid crystal device with their respective optic axesaligned with respect to the liquid crystal device such that the amountof light transmitted through the liquid crystal display will differdepending on which liquid crystal configuration is adopted.
 27. A liquidcrystal display as claimed in claim 25 wherein the means for opticallydistinguishing between at least two of the liquid crystal configurationsadopted comprises a optically reflective layer placed one side of theliquid crystal device and a polariser placed the other side of theliquid crystal device with its optic axis aligned with respect to theliquid crystal device such that the amount of light reflected by thedevice will differ depending on which liquid crystal configuration isadopted.
 28. A liquid crystal display as claimed in claim 25 wherein themeans for optically distinguishing between at least two of the liquidcrystal configurations adopted comprises a dichrioc dye, the dye beingadded to the liquid crystal such that the amount of light absorbed bythe liquid crystal display will differ depending on which liquid crystalconfiguration is adopted.
 29. A multi-stable liquid crystal devicecomprising a layer of liquid crystal material located between two cellwalls and a means of applying a voltage to the liquid crystal materialwherein a surface alignment grating structure on the internal surface ofat least one cell wall has a surface profile which is such so as toinduce the liquid crystal molecules to adopt any of three or more stablepretilt angles in the same azimuthal plane and wherein the arrangementis such that three or more stable liquid crystal molecularconfigurations can exist and wherein application of a suitable voltagecauses the liquid crystal material to adopt any one of three or morestable configurations.
 30. A multi-stable device as claimed in claim 29wherein three different pretilt angles in the same azimuthal plane canbe adopted.
 31. A multi-stable device as claimed in claim 29 wherein onecell wall has a multi-stable grating surface and the other cell wall hasa surface alignment grating surface profiled to permit the liquidcrystal molecules to adopt two different pretilt angles in the sameazimuthal plane.
 32. A bistable liquid crystal device comprising a layerof liquid crystal material located between two cell walls, a means ofapplying a voltage to the liquid crystal layer and a surface alignmentgrating on the internal surface of at least one cell wall wherein thesurface profile of the surface alignment grating comprises three or moredefect sites per grating period with at least one +½ defect site pergrating period and at least one −½ defect site per grating periodwherein one pair of +½ and −½ defect sites are situated so as to impartlow surface pretilt in the azimuthal plane to one defect state whereinsuch low pretilt state is of a significantly lower energy than that ofany of the other possible defect states wherein only the non-defectstate and the defect state of low pretilt can be readily selected onapplication of a voltage.